The recently appointed Tory chief whip Andrew Mitchell has been forced to apologise after an altercation with armed police in Downing Street that is alleged to have involved foul language.

Mitchell issued the apology following claims he was threatened with arrest for ranting at officers who prevented him leaving on his bicycle.

The Sun newspaper reported that Mitchell demanded: "Open this gate, I'm the chief whip. I'm telling you – I'm the chief whip and I'm coming through these gates." Tourists and other members of the public were said to have been within earshot.

The alleged incident, which happened just days after two police officers, Nicola Hughes and Fiona Bone, were shot dead near Manchester, is likely to cause embarrassment for David Cameron. The prime minister entrusted Mitchell with enforcing party discipline in this month's cabinet reshuffle.

Mitchell, a keen cyclist, denied using offensive language but admitted he had behaved badly after he was barred from leaving Downing Street via his usual route through the main gates.

In a statement he said: "On Wednesday night I attempted to leave Downing Street via the main gate, something I have been allowed to do many times before.

"I was told that I was not allowed to leave that way. While I do not accept that I used any of the words that have been reported, I accept I did not treat the police with the respect they deserve.

"I have seen the supervising sergeant and apologised, and will also apologise to the police officer involved."

A No 10 source said that Cameron was aware of the incident but was satisfied with Mitchell's apology.

"The prime minister believes the police should always be treated with respect," the source said.

Mitchell, a former UN peacekeeper, was promoted to chief whip from his position as international development secretary, a role he also occupied in Cameron's shadow cabinet. Mitchell was known by the nickname "Thrasher" as a tough prefect at Rugby public school. His reputation as a stickler for discipline is believed to have encouraged Cameron to hand him the Tory whip.

The former investment banker is said to be worth £2.2m, owning several properties including a house in the French ski resort of Val d'Isere and also one in his Sutton Coldfield constituency in Birmingham.